Mirrors and lenses (useful equations etc.)

Equations: §

1. For Flat Mirrors:

   • $d_o=d_i$
     • Used for: Describing the relationship between object distance and image distance in flat mirrors.
     • Where:
       • $d_o$: Object distance
       • $d_i$: Image distance

2. For Spherical Mirrors:

   • $f=\frac{R}{2}$

     • Used for: Determining the focal length of a spherical mirror.
     • Where:
       • $f$: Focal length
       • $R$: Radius of curvature

   • $\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$

     • Used for: Describing the relationship between focal length, object distance, and image distance for both concave and convex mirrors.
     • Where:
       • $f$: Focal length
       • $d_o$: Object distance
       • $d_i$: Image distance

3. For Thin Lenses:

   • $\frac{1}{f}=(n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

     • Used for: Lens-maker’s equation, it relates the focal length of a lens to the radii of curvature of its two surfaces.
     • For use in conjunction with a table of signs.
     • Where:
       • $f$: Focal length
       • $n$: Refractive index of the lens material
       • $R_1$: Radius of curvature for the first lens surface
       • $R_2$: Radius of curvature for the second lens surface

   • $\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$

     • Used for: Describing the relationship between focal length, object distance, and image distance for lenses.
     • Where:
       • $f$: Focal length
       • $d_o$: Object distance
       • $d_i$: Image distance

   • $M=-\frac{d_i}{d_o}$

     • Used for: Calculating the magnification of images through a thin lens.
     • Where:
       • $M$: Magnification
       • $d_o$: Object distance
       • $d_i$: Image distance

   • $\frac{1}{f_{eq}}=\frac{1}{f_1}+\frac{1}{f_2}$

     • Used for: Calculating the effective focal length when two thin lenses are in contact.
     • Where:
       • $f_{eq}$: Effective focal length of combined lenses
       • $f_1$: Focal length of the first lens
       • $f_2$: Focal length of the second lens

Sign Conventions: §

• For Mirrors and Lenses:
  • Object Distance:
    • Positive: Real Object
    • Negative: Virtual Object
  • Image Distance:
    • Positive: Real Image
    • Negative: Virtual Image
  • Focal Length:
    • Positive: Converging (for mirrors: concave, for lenses: convex)
    • Negative: Diverging (for mirrors: convex, for lenses: concave)